The fibre of a pinch map in a model category
Abstract
In the category of pointed topological spaces, let F be the homotopy fibre of the
pinching map X ∪ CA → X ∪ CA/ X from the mapping cone on a cofibration A → X
onto the suspension of A. Gray (Proc Lond Math Soc (3) 26:497–520, 1973) proved
that F is weakly homotopy equivalent to the reduced product (X, A)∞. In this paper
we prove an analogue of this phenomenon in a model category, under suitable
conditions including a cube axiom.